The flow diagram in Fig. 4 outlines the data acquisition and analysis approach adopted in this investigation, which consisted of several key steps. Initially, we performed surveys using an unmanned aircraft system (UAS) equipped with optical cameras and LiDAR sensors, along with a handheld laser scanner (HLS). Subsequently, the data collected during these surveys enabled the generation of a Digital Orthophoto Map (DOM), a bare-surface Digital Surface Model (DSM), a Digital Elevation Model (DEM), and 3D terrain point clouds. The drone imagery was processed with the Structure from Motion photogrammetry software Pix4D Mapper v4.5.6 (https://www.pix4d.com/, last access: 18 March 2026), while the open-source Cloud Compare v2.13.2 software (http://www.cloudcompare.org/, last access: 18 March 2026) was used to analyze the point clouds. ArcMap 10.5 was used to manually map the sinkholes and extract planimetric and three-dimensional morphometric parameters from the DOM, DEM and relief maps. This enabled the creation of a cartographic sinkhole inventory containing a number of categorical and numerical attributes for the morphometric and statistical analysis of the sinkholes. 3D data of the loess sinkholes, such as elevation and depth, were derived from noise-filtered terrain point clouds acquired with airborne LiDAR, rather than directly from the UAS-derived DSM, which significantly enhanced the accuracy of the parameters.

Drawing on a literature review on studies about loess sinkholes and karst dolines worldwide, we selected a number of morphometric parameters for the geometrical characterization of the loess sinkholes (e.g., Day, 1983; Liu and Wang, 2008; De Waele and Gutiérrez, 2022, and references therein). Table 1 presents the selected parameters, their definitions, and the approach used for their automatic computation. The key morphological parameters and their definitions are illustrated in Fig. 7.

Given the exceptionally high-resolution of the data used for mapping, the inventory can be considered nearly complete, even including small decimeter-scale holes. This information furnished a database of 1194 loess sinkholes in the study area, each characterized by multiple attributes (Table 1 and Data availability): topographic (coordinates, azimuth, maximum, minimum and average elevation); morphometric (length, width, depth, perimeter, area, volume, geometrical indexes); and geomorphic (soil loss). The inventory also differentiates 1162 single sinkholes, and 32 compound sinkholes resulting from the aggregation of two or more adjacent sinkholes. This comprehensive database serves as the basis for the morphometric-statistical analysis presented in this work. For the detailed cataloging and the statistical parameters of these sinkholes, please refer to Table 2 and Data availability. Additionally, 9 thematic maps were generated with some parameters (length, maximum depth, perimeter, area, volume, elongation ratio, circularity index, compactness index, length to depth ratio) to explore spatial patterns of different value ranges. Table 2 presents the main statistics of the sinkholes grouped into three categories: all, single, and compound.

The spatial distribution patterns of the loess sinkholes were analyzed considering their relationships with other geomorphic features (Fig. 3) and using spatial analysis and statistics tools (Fig. 8). The detailed geomorphological map of the Sunjiacha basin reveals that sinkholes are preferentially distributed in the following zones (Fig. 3): (1) the margins of the deeply entrenched lower-middle section of the Sunjiacha trunk stream; (2) tributary gully systems in the lower-middle part of the Sunjiacha basin; (3) landslides (slid mass and crown), mostly associated with the trunk channel; and (4) man-made terraces. The kernel density model in Fig. 8a shows low densities mainly associated with upper part of the Sunjiacha basin, where the drainage network shows a lower degree of incision, and rounded divides characterized by low local gradients. Overall, there is a good spatial correlation between sinkholes and areas with high local topographic gradients and loess deposits disturbed by landslides. The hot spot model based on sinkhole area shown in Fig. 8b illustrates a pronounced cluster of small sinkholes (cold spots in blue) associated with recent landslides in the lower sector of the basin. Clustering of large sinkholes (hot spots in red) mainly occur along the main drainages of tributary catchments in the lower part of the Sunjiacha basin.

In this section, we analyze the spatial and morphometric parameters computed for the 1194 inventoried sinkholes (1162 single, 32 compound), their frequency-size distribution (Fig. 9), as well as some spatial patterns based on the distribution of different value ranges (Fig. 10). It should be noted that the airborne LiDAR returned sparse and limited point clouds when detecting sinkholes with diameters less than 1 m. Consequently, for the calculation of parameters related to sinkhole depth and volume (e.g., Maximum Elevation, Maximum Depth, Volume, and Length-to-Depth Ratio), we retained only those 809 sinkholes with diameters ≥1 m.

The semi-log plot in Fig. 11 represents separately the length of the 1162 single sinkholes and the 32 compound sinkholes mapped in the Sunjiacha basin, versus relative cumulative frequency. The latter indicates the frequency of sinkholes equal or larger than a given length. The length distribution of the single sinkholes, ranging from 35.1 to 0.2 m and covering 2.3 orders of magnitude (i.e., log⁡(Max/Min)), shows a wider range than the compound sinkholes, spanning 1.6 orders of magnitude from 33.9 to 0.9 m. As expected, compound sinkholes tend to reach larger dimensions (i.e., plotted to the right), with a median length (cumulative frequency =0.5) that is 1.7 times larger than that of single sinkholes (3.8 vs. 2.2 m).

In both cases, the empirical cumulative frequency-size distribution can be modelled satisfactorily by logarithmic functions (natural logarithm) with a high goodness of fit (R2>0.97). The regression of the compound sinkholes describes adequately the distribution for the whole length range. In contrast, the empirical distribution of the single sinkholes deviates from the fitted curve for both small (<0.4 m) and large dimensions (>12.7 m). These cut-off or rollover points indicate lower empirical frequencies for the smaller sinkholes and higher frequencies for the larger ones compared to the regression curve. Given the completeness of the sinkhole inventory, the lower rollover can be attributed to physical constraints, such as the minimum span of a pipe-roof required for a collapse to occur. The upper rollover could be related to factors such as the expansion of single sinkholes and the depth distribution of sinkhole-forming underground pipes, which in the study area can reach significant depths given the considerable thickness of the loess cover. Note that sinkholes reach a maximum depth of 29.6 m.

The planimetric (length, width, perimeter, area) and three-dimensional (maximum depth, volume) size parameters of the sinkholes were fitted pairwise in a matrix diagram showing graphically and with regressions (power functions) the relationships between each pair of morphometric parameters (Fig. 12). As expected, the regressions of pairs of planimetric parameters have always high goodness of fit R2>0.94. In contrast, the relationship between planimetric and 3D parameters is poorer. R2 is always below 0.6 for maximum depth, and less than 0.9 for volume.

Sinkhole development, including cavity-roof collapse and the expansion of sinkhole margins by mass wasting processes, can contribute significantly to soil erosion, despite it is largely overlooked worldwide. The complete and accurate sinkhole inventory constructed in the Sunjiacha basin, including volumetric data, provides an excellent opportunity to assess the impact of sinkhole-related soil erosion within the context of the Loess Plateau. We calculated the soil loss associated with each sinkhole by multiplying the volume of each depression by the soil's dry bulk density, as shown in Fig. 13a. Figure 13b illustrates the frequency distribution of soil loss related to individual sinkholes: 0–1 t (389 sinkholes, 32.58 %); 1–14 t (211 sinkholes, 17.67 %); 14–177 t (361 sinkholes, 30.23 %); 177–2014 t (194 sinkholes, 16.25 %); 2014–24 973 t (39 sinkholes, 3.27 %). The aggregate volume of sinkholes (27.08×104 m3) multiplied by the soil's dry bulk density (1.27 tm-3) yields a total soil loss for the basin of 34.50×104 t. Considering the area of the basin (2400 ha), the specific soil erosion related to sinkholes can be estimated at 143.75 tha-1. Note that these values do not include hidden non-collapsed pipes. Figure 13a shows that the impact of the process is quite uneven, with a much greater contribution in the lower half of the basin and in the areas associated with deeply incised gullies.

Point clouds captured by airborne LiDAR surveys cover most of the sinkhole topography, thanks to the vertical orientation of the sensors. However, obtaining comprehensive point clouds of the interior of sinkholes remains challenging due to line-of-sight obstructions and the complex morphology. To address the limitations of airborne LiDAR scanning, we employed a handheld laser scanner to conduct a detailed investigation in the interior of thirteen representative sinkholes. Figure 14a–j shows the field photographs and 3D models of a loess sinkhole (HLS01). Morphometric measurements indicate that the perimeter of the sinkhole at the land surface is 49.7 m, with an area of 179.6 m2 and a maximum vertical depth of 20.1 m. We adopted both the traditional method and the point cloud slicing algorithm to estimate the volume of this sinkhole. The results show a volume and soil loss of 3610 m3 and 4585 t calculated by the former method, while the latter yielded values of 1750 m3 and 2223 t, respectively (Table 3). Because the fact that the sinkhole has an inclined top opening and a sloping bottom underlain by deposits (Fig. 14a and d), the volume calculated by the traditional method was twice higher than the actual volume. This finding also demonstrates that handheld laser scanning can capture the complete geometry of the sinkhole more accurately, overcoming the technical limitations of airborne LiDAR.

Interestingly, most sinkholes examined in the field display dominant vertical development, while this particular sinkhole exhibits a complex three-dimensional morphology comprising a vertical shaft connected to a subhorizontal pipe. The upper shaft-like portion of the sinkhole (20mlength×14mwidth×20.1mdepth) is situated in loess deposits, while the lower portion (14mlength×3.2mwidth×5.4mheight) is a gently inclined ellipsoidal conduit carved into horizontally bedded and jointed reddish sandstone. This lower conduit ends at the sinkhole outlet perched 8 m above the valley floor (Fig. 14a). Unfortunately, due to the lack of precise chronological evidence, we are unable to determine whether the initial development of this sinkhole predates or postdates the valley incision. We interpret that the development of this complex sinkhole started as a backward propagating conduit at the foot of the slope, associated with a seepage outlet point controlled by joints in the loess cover and the bedrock (Fig. 14d–h). Eventually, the enlarging conduit reached a sufficiently large span to initiate upward roof collapse, ultimately originating the sinkhole. At present, five distinct ceiling cupolas can be clearly observed at the top of this pipe (Fig. 14b, c and i), indicating sites of upward roof propagation (stoping).

Additionally, we observed a significant accumulation of horizontally stratified flood deposits resting atop the aeolian loess on the fluvial strath terrace (Fig. 14a). The interior of the sinkhole is relatively cool and damp, with the bottom underlain by collapsed soil. We found remnants of past flash-flood or debris-flow deposits on the sinkhole floor, as well as on the walls and outlet ceiling of the connected lateral pipe (Fig. 14d, f and j). These sediments may include: (1) Horizontally bedded deposits accumulated during floods in the drainage, with a stage high enough to cause the penetration of flood waters into the sinkhole outlet (backflooding); (2) Massive to poorly stratified deposits derived from collapse and mass wasting processes acting primarily in the pipe roof and sinkholes margins, respectively. It should be particularly noted that the largest loess landslide in this basin occurred on the opposite bank of this sinkhole. Based on field investigations, we believe that this landslide completely blocked the paleo-channel at that time, forming a small-scale dammed lake, and the landslide deposits and lacustrine sediments could easily have entered the interior of the sinkhole through lateral pipe.

The development of loess sinkholes is influenced by multiple factors of different nature, such as topography, climate, hydrology, soil texture, joints and fissures, animal activity, plant root systems, and human activity (Bernatek-Jakiel and Poesen, 2018; Peng et al., 2018; Geng et al., 2021; Hu et al., 2022; Kariminejad et al., 2023; Li et al., 2024). At the scale of a small basin, climate exhibits minimal variation. Therefore, we focus our analysis on the relationships between loess sinkholes and variables related to catchment topography, geomorphology, hydrology, and land use. In order to better understand the controlling factors, a number of topographic and geomorphic indices and variables, such as Slope, Total Catchment Area (TCA), Topographic Wetness Index (TWI), Valley Depth (VD), Channel Network Distance (CND), Landslides, and Landuse, were computed with the open-source SAGA GIS platform and subsequently mapped in ArcMap 10.5 (Fig. 15a–g). The selection of these indices and variables is primarily based on the following considerations: (1) Slope governs the inherent hydraulic gradient conditions for rainfall infiltration and surface runoff concentration, controlling the piping process leading to sinkhole development; (2) Total Catchment Area represents the upslope land surface that contributes surface and near-surface flow to a given outlet, pixel, or stream segment (Gallant and Hutchinson, 2011). It is a proxy for the potential volume of water that can reach a pipe or a sinkhole site, influencing on their initial formation and subsequent morphological evolution; (3) Topographic Wetness Index is a steady-state, terrain-based proxy for soil moisture and surface saturation potential. It quantifies the tendency of water to accumulate at any location by integrating local slope with the upslope contributing area (Moore et al., 1991); (4) Valley Depth is a measure of the vertical distance from a valley's highest ridges down to its lowest points. It is a proxy for the degree of dissection; (5) Channel Network Distance is the vertical height from a location to the nearest stream. Its value on valley margins depends on both gradient and planimetric distance to the nearest drainage; (6) Landslides can remodel the local topography and significantly disturb loess deposits, reducing their mechanical strength and increasing their permeability, which in turn promotes piping and sinkhole development; (7) Landuse mainly reflects the impact of human activity, notably terracing, on piping and sinkhole development.

In order to assess the spatial relationships between sinkholes and the different indices and variables, we calculated normalized frequencies for different intervals. This normalized frequency (Fn) is given by the ratio between the proportion of sinkholes in the interval and the proportion of the area of that interval. The higher the value of this “likelihood ratio”, the higher the spatial concurrence between sinkholes and the areas with values within the interval (Fig. 15a1–g1). These data, together with the findings presented in the results, help to shed light on the formation and spatial distribution of the loess sinkholes.

Overall, the normalized frequency graphs show that the distribution of sinkholes is primarily controlled by hydrological, topographic and geomorphic factors. Water availability is an essential factor, in as much as subsurface flow is the geomorphic agent responsible for piping development. This is illustrated by the higher normalized frequencies of sinkholes in areas with high Total Catchment Area (>100 m2; Fn=2.97) and high Topographic Wetness Index (>9; Fn=4.92). Slope is the main governing topographic factor, which largely determines hydraulic gradient and the erosional capability of subsurface flow. Sinkholes preferentially occur in high gradient areas and close to incised gullies, with high Slope (>40°; Fn=1.82), high Valley Depth ( m; Fn=1.98), low Channel Network Distance (<1 m; Fn=1.98), and areas primarily classified as erosional gullies (Fn=2.53). A good spatial correlation is also observed between sinkholes and landslides, with a normalized frequency of sinkholes within landslides (Fn=3.42). These spatial patterns are clearly recognizable in the detailed geomorphological map (Fig. 3) and the Kernel density (Fig. 8a) and hot spot maps (Fig. 8b). The latter shows that sinkholes developed on landslides tend to be smaller. This could be attributed to a younger age of those sinkholes, developed on a more recent geomorphic surface.

The vast majority of the sinkholes occur in erosional gullies (71.44 %, 853 sinkholes). This pattern is consistent with findings reported for soil pipes in other regions worldwide (Verachtert et al., 2010; Kariminejad et al., 2023). Incised gullies may foster the development of pipes and sinkholes through various mechanisms (Bernatek-Jakiel and Poesen, 2018; Peng et al., 2018): (1) they create steep hydraulic gradients; (2) they guide converging surface and subsurface drainage; (3) they favor the development of inlet points (e.g., unloading cracks) and outlet points for seepage flow. As shown in Fig. 6c–f, rows of sinkholes occur along the bottom of erosional gullies. These sinkholes can be connected through groundwater seepage channels, as confirmed by electrical resistivity tomography surveys in previous studies (Hu et al., 2022). It can be anticipated that, with the expansion and coalescence of the sinkholes, the gully will experience significant entrenchment and will turn into a drainage dominated by surface flow.

Another interesting feature is the close association between landslides and sinkholes in the Sunjiacha basin. Previous studies have shown that soil pipes in slopes can favor efficient drainage and, to some extent, help maintain slope stability (Pierson, 1983; Uchida et al., 2001; Sidle and Bogaard, 2016). However, the sinkholes mapped on the landslides have mostly formed after the development of the slope movements. The greater susceptibility of landslide ground to piping and sinkhole development can be attributed to several factors: (1) landsliding contributes to weaken the loess deposits; (2) the internal deformation of the landslide mass typically involves a bulking effect (dilation and volume expansion) accompanied by an increase in permeability; and (3) fissures and other pathways for focused water infiltration are common on landslides (Hu et al., 2020, 2022). At some sites, a causal relationship between landslides and sinkholes can be inferred, showing a cascading geomorphic effect. Figure 15f and f1 illustrate that landslides play an important role in the development of sinkholes. The distance to landslides seems to control the development of sinkholes, but this control effect gradually decays with increasing distance from the landslide boundary. Statistics show that as many as 251 sinkholes (accounting for 21 %) have developed within the landslides, making the landslide interior the second largest contributor to sinkhole formation (Fn=3.42). Approximately 43 % of sinkholes are distributed within the landslide and its outward 20 m buffer zone (Fn=1.87). The size of the sinkholes (e.g., length, area and volume), which can be considered as a proxy for their age, seems to be influenced by the age of the geomorphic surface. Mature sinkholes tend to be larger due to expansion and coalescence, and they usually occur on old geomorphic surfaces (such as old gullies, river terraces and ancient landslides). Conversely, sinkholes developed on landslides that have occurred in the past few years or decades tend to be smaller. This pattern is clearly depicted in the hot spot map shown in Fig. 8b.

We should be aware that the formation of soil pipes and sinkholes is not determined by a single factor, but rather results from the interplay of interconnected geomorphic processes and overlapping external influence factors (e.g., loess thickness, landscape position, surface and subsurface flow, impermeable base layers, etc.). Conversely, the development of soil pipes and sinkholes can further undermine slope stability, intensify gully erosion, and induce geological hazards such as collapses, landslides, and debris flows.

In recent decades, due to a significant decrease in the local agricultural population and the implementation of policies that promote the conversion of farmland back to forests and grasslands, approximately 74 % of the terraced fields have been taken out of cultivation. The landuse map (Fig. 15g and g1) shows that abandoned terraces have reverted to grasslands in the Sunjiacha basin. Abandoned terraces (25.63 %, 306 sinkholes) appear to be more prone to sinkhole formation than cultivated terraces (2.51 %, 30 sinkholes). This can be related to more favorable conditions for pipe development in the abandoned terraces and the lower preservation potential of the sinkholes in the cultivated terraces, where sinkholes tend to be filled soon after their formation. Without a doubt, pipe collapses and gully development pose threats to land productivity, agricultural sustainability, soil nutrient levels, and the carbon cycle, while also potentially destabilizing socio-economic conditions (Llena et al., 2024). By contrast, roads, bare land, and settlement sites seem to exert almost no influence on sinkhole occurrence.

Sinkholes tend to be elongated and preferentially oriented in the Sunjiacha basin (Fig. 9a and i). The majority of the major axes of the sinkholes align closely with the directions of the trunk (N–S) and secondary (E–W) channels in the watershed (Fig. 3). These directions tend to guide: (1) subsurface water flow and the trend of pipes generated by internal erosion, and (2) the orientation of unloading cracks (e.g., scarped channel margins) through which water can infiltrate. Both the pipes and the cracks influence the horizontal development of the sinkholes by mass wasting processes acting on the margins and through coalescence (e.g., the merging of aligned sinkholes connected to a common pipe).

The altitudinal distribution of sinkholes (Fig. 9d) may be governed by several factors: (1) the density and entrenchment degree of the drainage network are higher at lower elevations; (2) ground disturbed by landslides chiefly occurs in low elevation areas associated with the trunk Sunjiacha stream; (3) high-elevation zones (e.g., rounded drainage divides) generally have lower topographic gradient, lower degree of dissection, thinner loess cover, and more restricted runoff contributing areas.

The deeper and larger sinkholes tend to be distributed in the more deeply incised valleys (Fig. 10b and e). This pattern can be attributed to the development of deeper subsurface pipes in areas with thicker loess, greater topographic gradient and lower local base level. Thicker loess tends to accumulate in paleotopographic lows, which subsequently guide gully networks.

The goodness of fit between the planimetric and 3D parameters of the sinkholes is relatively poor (Fig. 12). This indicates a limited dependence between the horizontal and vertical dimensions of sinkholes, in agreement with the wide range shown by the Length to Depth ratio (0–6). That is, sinkholes with small area can have significant depth and volume, and sinkholes with limited volume can reach relatively large areas. This is also reflected by the relatively poor fit shown between the two 3D parameters (volume and maximum depth; R2=0.66). Even so, the fitting equations presented in Fig. 12 provide preliminary empirical support for characterizing and predicting scaling relationships for sinkholes in the Loess Plateau.

The cumulative frequency-size graph in Fig. 11 shows that the length distribution of the compound sinkholes (red) is clearly shifted towards larger dimensions with respect to the single sinkholes (green). The average length of the compound and single sinkholes is 7.37 and 3.65 m, respectively. This expected deviation in the size distribution can be explained by the different sets of processes that operate in the development of the two sinkhole populations. The size of the single sinkholes is related to pipe-roof collapse and the subsequent expansion of the scarped edge of the depressions by erosional processes, mainly mass wasting and gullying. The size tends to increase with the time elapsed since the initial collapse, as the sinkhole edge recedes. Compound sinkholes result from the coalescence of adjoining and expanding sinkholes and/or the occurrence of a new sinkhole intersecting a pre-existing one, leading to the sudden enlargement of the depressions. The contribution of these processes (coalescence, intersection) is influenced by the density and clustering degree of the sinkholes, in as much as the likelihood of sinkhole aggregation is greater in tightly clustered sinkhole populations (Bernatek-Jakiel et al., 2019; De Waele and Gutiérrez, 2022; Sevil and Gutiérrez, 2023). Moreover, sinkhole merging entails a decrease in sinkhole density by number and a substantial increase in sinkhole size.

Figure 11 shows the cumulative frequency-length distribution of the single and compound sinkholes mapped in the Sunjiacha basin, together with the single sinkholes inventoried in two catchments with contrasting geological and climatic conditions (Bernatek-Jakiel et al., 2019): Valpalmas in the Ebro Cenozoic Basin (NE Spain), and Tyskowa in the Bieszczady Mountains of the Outer Eastern Carpathians (Poland). The pipe collapses in Valpalmas occur in Holocene valley-fill alluvium consisting of indurated, Na-rich cohesive clayey silt that reaches around 8 m in thickness. Here, the climate is semiarid (mean precipitation 500 mm) and sinkholes tend to occur associated with the edge of erosional scarps, showing a tightly clustered distribution. The pipe collapses in the Tyskowa catchment can be considered as a representative sample of those inventoried in several catchments of the Bieszczady Mts., characterized by a humid climate (mean precipitation 900 m; Bernatek-Jakiel et al., 2019). Here, sinkholes occur on relatively thin slope deposits with some eolian component consisting of poorly indurated clayey silt. The single sinkholes in Valpalmas (orange) show a similar size to the single sinkholes in Sunjiacha for the central cumulative frequencies (i.e., Fc 0.5–0.6). Nonetheless, single sinkholes in Valpalmas display a much narrower length range (1.1 vs. 2.3 orders of magnitude, resulting in steeper curve) and significantly smaller maximum dimensions (6.5 vs. 35.1 m). The more restricted size range for the smaller sinkholes can be attributed to the fact that the inventory in Valpalmas was restricted to sinkholes with lengths ≥0.5 m. The differences between Sunjiacha and Valpalmas can be ascribed to factors such as the greater morpho-sedimentary diversity of Sunjiacha, where sinkholes occur in a broad range of deposits and geomorphic settings (e.g., loess, colluvium, alluvium), and the wide depth range of sinkhole-forming pipes, substantiated by the measured maximum depth of the sinkholes, ranging from 29.6 to 0.42 m (Figs. 9e, 10b and 14c). Single sinkholes in the humid Bieszczady Mts. of Poland are much smaller, mainly because they occur on thinner and mechanically weaker deposits. The weaker the soils, the smaller the largest span that can reach cavities before collapse. Induration of the deposits by secondary carbonate (i.e., cementation) in this humid environment is less significant than in the semiarid environments of Valpalmas and the Loess Plateau.

Extensive field surveys reveal that loess sinkholes possess highly complex three-dimensional morphologies, rather than being simple cylindrical or conical features (Figs. 6i, 7c, 14b and 16; Hu et al., 2024). This is illustrated by the high-resolution scanning of 142 sinkholes with a handheld laser device carried out in 2021 in a small basin, named Laozigou, east of our study area (Hu et al., 2024; Jiang et al., 2024). The data can be accessed at 10.1016/j.geomorph.2024.109404. As shown in Table 3, volume estimates based on airborne LiDAR point clouds and simplified volume estimation methods can lead to highly inaccurate approximations. The aggregate volume, and hence the inferred soil loss reported in our study area may therefore be overestimated. Several factors may contribute to the deviation between the actual volume and the volume calculated, leading to over- or under-estimations: (1) volumes are calculated using maximum depth and assuming a cylindrical geometry, but sinkholes may be conical (overestimation) or the actual depth may be deeper (underestimation); (2) sinkholes may be connected to conduits that cannot be imaged in airborne surveys, resulting in underestimations.

Encouragingly, the comprehensive point clouds acquired by the handheld scanner enable us to develop far more precise cloud-slicing and volumetric-integration algorithms for exact volume computation (Hu et al., 2024). This will enable us to develop a more reliable fitting formula relating sinkhole area and volume, which could be used for refining the results obtained from the UAS surveys. We conducted a survey of a gully by jointly employing UAS-LiDAR and HLS-LiDAR technologies and found that the integrated point cloud data can effectively delineate the internal structure and connectivity of sinkholes, as they overcome the limitations of a single LiDAR technology. Meanwhile, machine-learning approaches for the automatic detection and delineation of sinkholes are rapidly emerging and showing promising results (Zhu et al., 2016, 2020; Jiang et al., 2024; Li et al., 2024; Coşkuner et al., 2025; Creati et al., 2025). Indeed, we have already implemented an end-to-end workflow that couples airborne LiDAR point clouds with deep-learning models to achieve automatic sinkhole identification, instance segmentation, feature extraction, cataloguing, and mapping (Li et al., 2025).